How do I know how many shares will Infosys pick up and by which date. I have not got any letter from the Registrar or Infosys itself on this.

The number of shares Infy will pick up for the buyback will depend on the acceptance ratio - decided by the number of shareholders applying for the buyback and the number of shares they tender. The acceptance ratio can be calculated only after the buyback window period closes. Then this ratio should be declared by the RTA and the remaining unaccepted shares will be credited back to your Demat.